NCERT Solution for Class 8 Maths-Rational Numbers
Class 8 Maths – Rational Numbers : In mathematics, we usually come across different terms like natural number, whole numbers, integers and rational number. We will discuss rational number in this article from 8th Class Maths.
Let’s us revisit the properties of Rational numbers in class 8.
A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0.
Properties of Rational numbers
We will first discuss the properties of rational numbers.
We call a set of numbers closed under operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case we also say that the set is closed under the operation.
Rational numbers are closed under addition.For any two rational numbers a and b,a+b is also a rational number.
Rational numbers are closed under addition.For any two rational numbersaand b, a-b is also a rational number.
Rational statistics are closed under multiplication.For any two rational numbers a and b, a*b is also a rational number.
Rational numbers are not closed under multiplication.For any rational number a, a/0 is not defined.
As per commutative property, the interchanging order of numbers will not change the result.
Two rational numbers can be added in any order.Addition is commutative for rational numbers.For any two rational numbers a and b, a+b=b+a
Subtraction is not commutative for rational numbers.
Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a
Division is not commutative for rational numbers
Addition is associative for rational numbers.For any 3 rational numbers a,b, and c.
a + (b+c) = (a+b) +c
Subtraction is not associative for rational numbers
Multiplication is associative for rational numbers.For any 3 rational numbers a,b, and c.
a *(b * c) = (a * b) *c
Division is not associative for rational numbers.
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The Role of Zero
Zero is called the identity for the addition of rational numbers.It is the additive identity for integers and whole numbers as well.
The role of 1
1 is the multiplicative identity of rational numbers.
Negative of a number
For any rational number a/b, we have a/b+(-a/b)=(-a/b)+a/b=0.We say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse of (-a/b).
A rational number c/d is called the reciprocal or multiplicative inverse of another rational number a/b, if a/b*c/d=1.
Distributive property of multiplication over addition and subtraction
For all rational numbers a,b, and c
a (b+c)=ab+ ac
Rational Numbers between two rational numbers
Let’s consider the below example for 8th class maths
Q – Find rational number -1/10 and 3/10?
Sol- Rational numbers -1/10 and 3/10 are
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